Subjects

Twenty patients (5 males and 15 females, mean age 22 years; range 16 years 4 months to 28 years 9 months) from the orthodontic clinic of Health Sciences University of Hokkaido were selected. They were diagnosed as having skeletal Class III malocclusion with facial asymmetry and did not have congenital craniofacial anomalies or missing teeth. They had deviation in Me of more than 2 mm from a line perpendicular to Lo-Lo′ that passed through CG in posteroanterior cephalometric radiography (range 2.2 to 15.7 mm). In addition, 70% of the subjects (2 males and 12 females) were diagnosed as having internal derangement of the temporomandibular joint (TMJ). These patients exhibited TMJ noise on opening their mouth, sometimes with pain (bilateral, 50%; unilateral-deviation side, 43%; unilateral-opposite side, 7%). All subjects were informed of the experimental protocols and signed an informed consent form that was previously approved by the Institutional Review Board. The subjects' rights were protected at all times.

Cephalometric analysis

Each pretreatment posteroanterior cephalometric radiograph was scanned using a flathead scanner (GT-9000, EPSON, Tokyo, Japan), and landmarks were identified directly on the digital image using image-analysis software (NIH Image; developed at the U.S. National Institutes of Health). The measurement error was checked on the digital images by the repeated identification of all landmarks. The x and y coordinates were calculated separately using the formula: error = .

The error was within 0.1 mm for the X coordinate and within 0.1 mm for the Y coordinate. Landmarks and planes in posteroanterior cephalometric radiography are shown in Figure 1. The lateral deviation of Me was measured as the distance from a line perpendicular to Lo-Lo′ that passed through CG. The angle between the Lo-Lo′ plane and the J-J′ plane was measured.

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Dental cast analysis

A three-dimensional surface-scanning system using a slit laser beam (VMS-150RD, UNISN, Osaka, Japan) was used to measure the dental casts. We had reported the reliability of this measuring device,13 and in this study we have provide a summary in the “Discussion.” The system consisted of a slit laser projector, two charge-coupled device cameras, an autorotating mounting unit, and a personal computer with postprocessing software. The resolution in the X-direction was 0.01 mm, and the Z-direction could be measured to within ±0.05 mm. The three-dimensional shape data-analysis system consisted of a graphical workstation (Zx1, Intergraph, Huntsville, AL) and data processing and analyzing software (I-DEAS, SDRC, Milford, OH).

Each maxillary dental cast was measured by the three-dimensional surface-scanning system with a measuring pitch of 0.25 mm, and the palatal reference plane was calculated.12 The three-dimensional shape data from the dental cast were segmented on the basis of differences in mean curvature H (1/mm: the curvature is the reciprocal of the radius of curvature). The flatter region of the palatal surface was extracted after setting a threshold (0 < H < 0.21). The extracted region was composed of 2000–3000 points, and the flat plane was fitted by the least-squares method. Fitting was carried out automatically by searching for the minimum amount of mismatch between the extracted region and a flat plane. Therefore, it was possible to define the palatal reference plane.

First, the right/left difference in the radius of curvature of the palate was analyzed. The palate shape data for the posterior teeth (15 mm anterior from the distal surface of the first molars) were divided into right and left sides by the median palatal raphe, and the data were subdivided into 10 cross-sectional lines. Each angle between a midline determined by the median palatal raphe to the subdivided lines was 90°. The radii of curvature were approximated using the least-squares method. Therefore, the mean values of radii of curvature for lines 1 to 10 (Figure 2) were calculated. Next, the right/left differences in the vertical and mesiodistal positions of the first molars were analyzed. The vertical position was measured as the linear distance from the reference plane to the tip of the mesiolingual cusp, and the mesiodistal position was measured as the linear distance from the YZ-plane to the tip of the mesiolingual cusp (Figure 3).

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Statistical analysis

Linear correlation and regression tests were used to evaluate relationships between the lateral deviation of Me and the J-J′ plane angle in posteroanterior cephalograms, the right/left difference in the radius of curvature of the palate, and right/left differences in the vertical and mesiodistal positions of the first molars in the three-dimensional analysis of dental casts.

Reliability of the analysis method

We had reported the reliability of the three-dimensional measuring device used in this study.13 A calibrating plane plate was measured using the device, and the best-fit expression for the plane was calculated from the entire data, to within ±3 SD, by the least-squares method. The reliability of the measurement was evaluated by calculating the maximum error between the calculated plane and the obtained data. The result was ±0.05 mm. Therefore, the reliability of the three-dimensional measuring device is sufficient for dental cast analysis. We also had reported the reliability of the newly defined palatal reference plane used in this study.12 The newly defined palatal reference plane in the three-dimensional dental cast analysis corresponds to the A-PNS plane in a lateral cephalogram and to the J-J′ plane in a posteroanterior cephalogram, which have been shown to be sufficiently accurate as references for measurement.

Characteristics of skeletal asymmetry

Facial asymmetry is not rare.14 Shah and Joshi15 reported that even pleasing and apparently symmetrical faces exhibit skeletal asymmetry. Farkas and Cheung16 used anthropometry to measure normal facial asymmetry and noted that although asymmetries were not always obvious, they were common. Haraguchi et al3 reported that facial asymmetry was found in 70–85% of subjects with skeletal Class III deformity. They considered subjects to have asymmetry if they had a deviation of more than 2 mm from the facial midline associated with any of the landmarks. In this study, we selected subjects who had skeletal Class III deformity with a deviation in Me of more than 2.0 mm from a line perpendicular to Lo-Lo′ that passed through CG.

Although there is no clear explanation of the etiologic force underlying facial asymmetry, trauma, infection, and TMJ disorder must be considered when encountering facial asymmetry121718; 70% of the subjects in this study had temperomanibular disorder (TMD). Many morphological characteristics of facial asymmetry have been reported,19 and asymmetry is apparently more remarkable in the lower one-third of the face than in the middle.14 In this study, a similar trend was detected between the lateral deviation of Me and the J-J′ plane. In our analysis using only postero-anterior cephalometric radiographs, it was difficult to obtain detailed information on the palate form and the axis of buccal teeth. As a solution to this problem, computerized tomography (CT) scan is better for acquiring three-dimensional information.20–22 However, the level of radiation is too high for routine use.

As another option, advances in measuring devices and the use of computers have greatly improved three-dimensional dental cast analysis.9–13 In this study, a significant correlation was found between the lateral deviation of Me and the right/left difference in the radius of curvature of the palate in the posterior teeth (P < .001) and the right/left difference in the vertical position of the first molars (P < .01). These findings demonstrate that the compensation for lateral deviation of the mandible is closely related to the morphology of the alveolar process and dentition. This supports findings that the inclination of the occlusal plane is closely associated with facial asymmetry.619 A correlation was not found between the right/left difference in the mesiodistal position of the first molars. This result also indicates that vertical asymmetry in the maxillary dental arch significantly affects facial asymmetry. However, one of the most critical limitations of this study might be that we did not perform an evaluation on the basis of submentovertex radiography. Therefore, horizontal asymmetry of the maxillary dental arch based on cranial base structures was not evaluated.